Infimal convolution and optimal time control problem III: minimal time projection set

Abstract

We continue the investigation of a general minimal time problem with a convex constant dynamics and a lower semicontinuous extended real-valued target function defined on a Banach space. In this paper we obtain an explicit description of the minimal time projection set in terms of the Legendre-Fenchel conjugate function and provide some sufficient conditions for this set to be nonempty. The single valuedness and Lipschitz property of the minimal time projection are also investigated.